Your not likely going to get an idea of cost before you have more details. Costs change from area to area, so the cost would be a local thing.
You should not plan on building on top of the driveway, especially if it is to be tied to the house.
So you would start by developing a plan, size, shape, style and how it ties to the house and how the roof ties to the house roof and so on. The city may have something to say about it too.

Well, the driveway connects to the house. So if it isn't built over that concrete they will just have to tear half of the driveway up. Also, we don't live in an independent city. It would be a 1 door 2 car garage